# variation

1. ### variation of parameter

For this question, when we integrate x with d(y' + 3y)= e^(-4x) +4y with x , we got y' +3y= e^(-4x)/-4 + 4yx, we are unable to get f(x) , there is 4xy, ihow to solve this question??
2. ### Variation of Parameters work check

Can someone check my work and see what I did wrong. This is an initial value problem. Here's the question and my answer: Here's my work. Sorry if it is hard to read.
3. ### variation of parameter

in step2 , why thw y1 not equal to Acosx ? y2 not equal to Bsinx ? for second photo , why the author assume B+1 = B ?
4. ### Standard Deviation and Coefficient of Variation

This is a sample problem for study purposes only: I have the solution to the Building A: but I am not sure how the numbers fit in the formula --I just need help understanding the concept and how it is used in this case in the most simple way possible. Also, Where did the ^5 come from? When I...
5. ### Trouble understanding method of variation of parameters

Problem: y'''-3y''+4y = e^2x, solve using method of variation of parameters. Aux polynomial: r^3 -3r^2+4 = (r+1)(r-2)^2 therefore Y(homogeneous) = ae^-x + be^2x +cxe^2x. Now normally I would just take a guess at the particular solution and say its of the form: Ax^2e^2x. Then I would find...
6. ### variation of parameter to find second solution

(1+t)^{3} \frac{d^{2}x}{dt^{2}}-(1+t)\frac{dx}{dt} + x = 0 i) show that x(t) = 1+t is a solution to this ODE ii) use variation of parameters to find another solution to this ode ie. write x(t) = c(t)(1+t) and fint c(t) I need help with part (ii) x(t) = (1+t) x'(t) = 1 x''(t)...
7. ### law of total probability - variation formal names?

Hello, there are different variations of the law of total probability. For example, the probability of 3 discreet events all occurring is: A1 * A2 * A3 The probability of at least 1 of 3 discreet events occurring is: 1 - ((1 - A1) * (1 - A2) * (1 - A3)) Is there a formal name...
8. ### Good reference on multi-variable calculus of variation

I am looking for a good and easy access reference on multi-variable calculus of variation with many examples and demonstrations. Although I have many books and references on the calculus of variation, most are focused on single-variable. Any advice will be appreciated.
9. ### What is the derivative of total variation?

Let f(x) be a function of bounded variation on closed, bounded interval [a, b]. Let g(x) = V(f, [a, x]) where V(f, [a, x]) = \sum_{k=1}^n |f(x_{i}) - f(x_{i-1}) | given some partition P = \left \{a, x_{1}, x_{2}, ...., x_{n-1}, x \right \} of [a, x]. How can I calculate the derivate of...
10. ### function fo bounded variation!

find P_{f}= [-1,2], N_{f}= [-1, 2] and T_{f}= [-1,2] if given that f(x)= |x|+1 for -1\leq x \leq 2 effort made; given that f(x)=|x|+1 for -1\leq x \leq 2 we have f(-1) = 2 f(2) = 3 so P_{f}[-1,2]= \sum_{j=1}^{2}[3-2]^{+} = [1]^{+} please help...
11. ### Variation on Recursive Bayesian Estimation

Hi, I'm doing a research on a variation of Recursive Bayesian Estimation- it's a Bayesian estimation with a 'time smoothing' term: { \hat { P } }_{ k+1 }(x)\quad =\quad \eta \cfrac { { \hat { P } }_{ k }(x)p({ z }_{ k+1 }|x) }{ \int _{ -\infty }^{ \infty }{ { \hat { P } }_{ k }(x)p({ z }_{...
12. ### Joint variation

Joint variation + percent The weight (W) that can be supported by a wooden beam varies directly as the square of its diameter (d) and inversely as its length (l). a) What percentage increase in the diameter would be necessary for a beam twice as long to support an equivalent weight? b)What...
13. ### Solving a DE by method of variation of parameters

I have found the general solution for the equation of y'' - 9y = (x+1) e^{-x} to be y(x) = A e^{3x} + B e^{-3x} - \frac{1}{8} e^{-x} x - \frac{3 e^{-x}}{32} by the method of undetermined coefficients. However I need to use the method of variation of parameters, but I am totally confused. I...
14. ### Variation

"A varies directly with B when C is constant and inversely with C when B is constant. A=6, B=2 and C=3. What is the value of A when B = 3 and C= 18?" What I really don;t know here is how to form the equation/ statement. I've never really come acroos this question. Thanks :)

16. ### Graduate Research (how much variation can I have?)

I am currently working on a graduate research paper and statistics is not something I'm good at. In my proposal I need to compare the STAAR test scores of two schools. The demographics of the schools need to be representative of the average Texas school. African American 14%, Caucasian 35%...